How this instrument works
A lens's power, in diopters, describes how strongly it bends light, but that number is only meaningful at the plane where the lens actually sits. Move the same optical correction from 12 millimetres in front of the cornea, where a spectacle lens rests, to the corneal surface itself, where a contact lens rests, and the vergence it delivers to the eye's far point changes even though the lens's curvature hasn't. The vertex distance formula, Fc = F ⁄ (1 − d·F), converts one into the other by tracking how vergence propagates across that gap.
The correction shrinks in magnitude for minus, myopic prescriptions and grows for plus, hyperopic ones, because the (1 − d·F) denominator affects the two cases oppositely. A −6.00 D spectacle lens becomes roughly −5.60 D as a contact lens, about seven percent weaker, while a +6.00 D spectacle lens becomes closer to +6.47 D as a contact lens, stronger rather than weaker. That asymmetry is real, not a rounding artifact; it falls straight out of the algebra of the denominator flipping which side of 1 it sits on.
Below roughly ±4.00 D the shift is smaller than the 0.25 D steps contact lenses are actually stocked in, so many practices skip the conversion for mild prescriptions and prescribe the spectacle number unchanged. Past that threshold, and especially past ±8.00 D, skipping it leaves a patient measurably over- or under-corrected, which shows up as blur, eye strain, or an unexplained struggle to adapt to a contact lens power that was never actually right for the corneal plane.
- Enter the prescription's sphere power into Spectacle (glasses) power, D — negative for myopia, positive for hyperopia.
- Set Vertex distance to the gap between the spectacle lens and the cornea; 12 mm is the common average and the field's default.
- If the dispensing record gives a measured distance instead, such as 10 or 14 mm, switch the unit menu and enter that figure.
- Read Equivalent contact lens power, D — the power a contact lens needs at the corneal plane to match the same correction.
Worked example — a −6.00 D prescription at 12 mm
A patient's glasses measure −6.00 D of sphere power, refracted at the standard 12 mm vertex distance, so F = −6 and d = 0.012 once the 12 mm is expressed in meters. Feeding those into Fc = F ⁄ (1 − d·F) gives Fc = −6 ⁄ (1 − 0.012 × −6) = −6 ⁄ 1.072 = −5.59701492537 D, which the field rounds for display to about −5.60 D.
That 0.40 D gap between −6.00 D of glasses and −5.60 D of contact lens is exactly the difference a fitter has to account for once a prescription passes about ±4.00 D. Order a stock −6.00 D contact lens instead of the corrected −5.60 D, and the patient carries about 0.40 D too much minus power, which is enough to blur distance vision and provoke eye strain during sustained near work.
Questions
Why does the same prescription need a different number for contacts than for glasses?
Because a lens's power is only defined at the plane where it sits, and a contact lens sits about 12 mm closer to the eye than a spectacle lens does. Moving the correcting surface that close changes the vergence it delivers to the eye's far point even though the prescription itself hasn't changed, so the vertex distance formula recalculates the power needed at the new plane.
How do I know what value to use for vertex distance?
12 mm is the conventional average and the field's default, close enough for most standard spectacle frames. If the dispensing record states a measured distance, commonly somewhere between 10 and 15 mm, use that figure instead; the formula is sensitive enough that a few millimetres shift the result noticeably for strong prescriptions.
Why does the correction shrink for minus prescriptions but grow for plus ones?
Because minus lenses diverge light and plus lenses converge it, and the (1 − d·F) denominator affects those two cases oppositely. For F negative the denominator grows above 1, shrinking Fc's magnitude; for F positive the denominator shrinks below 1, enlarging Fc's magnitude. A −6.00 D spectacle lens becomes about −5.60 D as a contact lens, while a +6.00 D one becomes about +6.47 D.
Is the vertex distance adjustment worth bothering with for a mild prescription?
Usually not. A −2.00 D spectacle prescription converts to about −1.95 D as a contact lens, a 0.05 D shift smaller than the 0.25 D steps contact lenses are actually manufactured in, so it rounds away in practice. The adjustment starts to matter clinically past roughly ±4.00 D and becomes significant past ±8.00 D.
Where does the F / (1 − d·F) formula actually come from?
It's the standard vergence-transfer relation from geometric optics: if a lens produces vergence L at its own surface, that vergence becomes L ⁄ (1 − dL) after travelling a further distance d through the same medium, since 1/L' = 1/L − d models how vergence changes with propagation. Setting L to the spectacle power F and d to the vertex distance gives exactly the formula this instrument evaluates.
Does this formula still apply to very high prescriptions, like ±15.00 D?
Mathematically yes, the same F ⁄ (1 − d·F) relation holds at any power, and it's exactly where the adjustment matters most, sometimes exceeding a full diopter of difference. Clinically, very high powers also bring lens-thickness and prismatic effects the thin-lens formula ignores, so practitioners still confirm the final contact lens power with an over-refraction on the eye.